This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A384124 #10 May 22 2025 16:57:23
%S A384124 1,1,1,1,2,1,1,4,4,1,1,8,9,8,1,1,16,24,24,16,1,1,32,77,94,77,32,1,1,
%T A384124 64,178,284,284,178,64,1,1,128,373,624,777,624,373,128,1,1,256,724,
%U A384124 1234,1620,1620,1234,724,256,1,1,512,1331,2258,3049,3286,3049,2258,1331,512,1
%N A384124 Array read by antidiagonals: T(n,m) is the number of irredundant sets in the n X m rook complement graph.
%H A384124 Andrew Howroyd, <a href="/A384124/b384124.txt">Table of n, a(n) for n = 0..1325</a> (first 51 antidiagonals)
%H A384124 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IrredundantSet.html">Irredundant Set</a>.
%H A384124 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RookComplementGraph.html">Rook Complement Graph</a>.
%F A384124 T(n,m) = n*(2^m-1) + m*(2^n-1) - n*m + binomial(n,2)*binomial(m,2) + 6*binomial(n,3)*binomial(m,3) + 6*binomial(n,2)*binomial(m,3) + 6*binomial(n,3)*binomial(m,2) + 6*binomial(n,4)*binomial(m,2) + 6*binomial(n,2)*binomial(m,4) + 1 for n >= 4, m >= 4.
%e A384124 Array begins:
%e A384124 ===============================================
%e A384124 n\m | 0 1 2 3 4 5 6 7 ...
%e A384124 ----+------------------------------------------
%e A384124 0 | 1 1 1 1 1 1 1 1 ...
%e A384124 1 | 1 2 4 8 16 32 64 128 ...
%e A384124 2 | 1 4 9 24 77 178 373 724 ...
%e A384124 3 | 1 8 24 94 284 624 1234 2258 ...
%e A384124 4 | 1 16 77 284 777 1620 3049 5332 ...
%e A384124 5 | 1 32 178 624 1620 3286 6022 10268 ...
%e A384124 6 | 1 64 373 1234 3049 6022 10771 17962 ...
%e A384124 7 | 1 128 724 2258 5332 10268 17962 29366 ...
%e A384124 ...
%o A384124 (PARI) T(n,m) = {n*(2^m-1) + m*(2^n-1) - n*m + if(n>2&&m>2,6,if(n+m>4, 2))*binomial(n,2)*binomial(m,2) + 6*binomial(n,3)*binomial(m,3) + if(m>3,6*binomial(n,2)*binomial(m,3)) + if(n>3,6*binomial(n,3)*binomial(m,2)) + 6*binomial(n,4)*binomial(m,2) + 6*binomial(n,2)*binomial(m,4) + 1}
%Y A384124 Main diagonal is A291622.
%Y A384124 Columns 0..2 are A000012, A000079, A290710.
%Y A384124 Cf. A384123.
%K A384124 nonn,tabl
%O A384124 0,5
%A A384124 _Andrew Howroyd_, May 22 2025